Dynamic prediction intervals for survival times
Abstract
Most work on survival prediction focuses on estimating survival probabilities rather than predicting individual event times. Recent conformal methods have made it possible to construct prediction intervals for survival times with right-censored outcomes, but existing approaches are restricted to settings with covariates only measured at baseline and do not address dynamic prediction with longitudinal data. We study prediction intervals for survival times in a dynamic prediction framework with longitudinal covariates. Our approach uses Penalized Regression Calibration (PRC) as a working dynamic prediction model, combining linear mixed models for the longitudinal histories with a Cox model for post-landmark survival, and then applies a conformal calibration step to obtain prediction intervals. We compare naive intervals obtained by direct inversion of the survival function estimated by PRC to our dynamic conformal method. A Monte Carlo simulation study evaluates empirical coverage and interval length across sample sizes, censoring levels, landmark times, and non-proportional hazards (NPH) scenarios. We illustrate the proposed methodology by computing dynamic prediction intervals for the time until a dementia diagnosis in the ADNI dataset. The results show that naive inversion is often unreliable, whereas the proposed dynamic conformal method yields more stable predictive performance.
Related
- Proper scoring rules for survival times
- Mean-Tilted Intervals: Regression and Dynamic Models
- CASCADE Conformal Prediction: Uncertainty-Adaptive Prediction Intervals for Two-Stage Clinical Decision Support
- PICPIs: Prediction-Interval-Conditional Prediction Intervals
- Frequentist prediction intervals for random-effects meta-analysis via confidence-distribution propagation
BibTeX
@misc{carvisiglia2026dynamic,
title = {{Dynamic prediction intervals for survival times}},
author = {Lorenzo Carvisiglia and Saverio Ranciati and Mirko Signorelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10409},
eprint = {2609.10409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10409},
}
RIS
TY - UNPB
TI - Dynamic prediction intervals for survival times
AU - Lorenzo Carvisiglia
AU - Saverio Ranciati
AU - Mirko Signorelli
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10409
UR - https://arxiv.org/abs/2609.10409
AB - Most work on survival prediction focuses on estimating survival probabilities rather than predicting individual event times. Recent conformal methods have made it possible to construct prediction intervals for survival times with right-censored outcomes, but existing approaches are restricted to settings with covariates only measured at baseline and do not address dynamic prediction with longitudinal data. We study prediction intervals for survival times in a dynamic prediction framework with longitudinal covariates. Our approach uses Penalized Regression Calibration (PRC) as a working dynamic prediction model, combining linear mixed models for the longitudinal histories with a Cox model for post-landmark survival, and then applies a conformal calibration step to obtain prediction intervals. We compare naive intervals obtained by direct inversion of the survival function estimated by PRC to our dynamic conformal method. A Monte Carlo simulation study evaluates empirical coverage and interval length across sample sizes, censoring levels, landmark times, and non-proportional hazards (NPH) scenarios. We illustrate the proposed methodology by computing dynamic prediction intervals for the time until a dementia diagnosis in the ADNI dataset. The results show that naive inversion is often unreliable, whereas the proposed dynamic conformal method yields more stable predictive performance.
ER -